Avon’s board may not have relished the idea of selling the company to a smaller rival, especially one that was prepared to sell itself to Avon only months before. But the evaporation of any deals means a lot of hard work may be ahead.

Avon’s new chief executive, Sherilyn S. McCoy, must figure out a way to turn around the company’s fortunes while operating under the cloud of a bribery investigation that has lasted years. It is unclear when the company’s own inquiry will conclude, let alone investigations by regulators.

Before coming to Avon, Ms. McCoy was a highly regarded executive at Johnson & Johnson with a focus on operations. She faces an uphill battle with Avon. Nearly every financial metric at the company declined in the first quarter: total revenue fell 2 percent from the prior year, and net income attributable to the company plunged 82 percent. Pro forma operating margins declined 6.1 percent as well.

Coty had argued that a deal could have injected both a strong management team and an array of celebrity-branded and high-end products that could have meshed well with Avon’s direct-sales business model.

People close to Avon contend that they were never sure how serious Coty was. While Coty, a privately held cosmetics company, boasted of its impressive firepower — including equity contributions from Warren E. Buffett‘s Berkshire Hathaway and the German conglomerate Joh. A. Benckiser, as well as debt financing from JPMorgan Chase — it hadn’t signed official commitment letters. And Coty appeared unwilling to pursue a deal at any cost, including by taking the matter directly to Avon shareholders.

For their part, Coty and its coterie of advisers felt that they were never given a fair shake. It went public with its bid after months of negotiations had gone cold, and complained privately that Avon never appeared willing to countenance even talks. The company also felt that, with the mountain of legal troubles confronting its target, it had to tread carefully instead of wholeheartedly throwing significant resources into an offer.

The final straw came on Sunday, when Avon asked for a week to consider Coty’s revised $10.7 billion offer instead of finally coming to the table. To Coty, that move felt like stalling rather than a constructive step toward negotiations.

It is unclear whether Avon should now be considered in play. Other cosmetics players had expressed little apparent interest in making a run for the company before Coty. And while media reports have speculated that the privately held conglomerate Richmont Holdings may be preparing a bid, so far nothing has emerged.

Coty is likely to continue its strategy of acquiring smaller cosmetics makers, according to people close to the company. Its Avon bid was something of an aberration, as none of its deals have surpassed more than about $1 billion.

Among Coty’s focuses will be expanding into developing markets like Brazil, one reason why it pursued Avon. People close to Coty have said that Avon’s direct-sales representatives — once known as Avon ladies — were an attractive sales model in that country and could have made for a good complement to Coty’s branded products.

And at some point it will seek to go public, as it had been considering before the opportunity to merge with Avon arose.